Simplify the following expression: $ z = \dfrac{-5r}{r - 9} + \dfrac{10}{7} $
Explanation: In order to add expressions, they must have a common denominator. Multiply the first expression by $\dfrac{7}{7}$ $ \dfrac{-5r}{r - 9} \times \dfrac{7}{7} = \dfrac{-35r}{7r - 63} $ Multiply the second expression by $\dfrac{r - 9}{r - 9}$ $ \dfrac{10}{7} \times \dfrac{r - 9}{r - 9} = \dfrac{10r - 90}{7r - 63} $ Therefore $ z = \dfrac{-35r}{7r - 63} + \dfrac{10r - 90}{7r - 63} $ Now the expressions have the same denominator we can simply add the numerators: $z = \dfrac{-35r + 10r - 90}{7r - 63} $ $z = \dfrac{-25r - 90}{7r - 63}$